Question: Solve for $x$ and $y$ using elimination. ${2x+2y = 30}$ ${-5x-2y = -57}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $2y$ and $-2y$ cancel out. $-3x = -27$ $\dfrac{-3x}{{-3}} = \dfrac{-27}{{-3}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {2x+2y = 30}\thinspace$ to find $y$ ${2}{(9)}{ + 2y = 30}$ $18+2y = 30$ $18{-18} + 2y = 30{-18}$ $2y = 12$ $\dfrac{2y}{{2}} = \dfrac{12}{{2}}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {-5x-2y = -57}\thinspace$ and get the same answer for $y$ : ${-5}{(9)}{ - 2y = -57}$ ${y = 6}$